Applications of Physics-informed Neural Networks on Computational Fluid Dynamics
Prof Ming-Jyh Chern
National Taiwan University of Science and Technology
Abstract: Recently, machine learning has received plenty of attentions due to the fast progress of GPU computing. However, machine learning needs many data to simulate a system. For a problem lack of data, physics-informed neural networks (PINNs) was proposed by Raissi et al. [1]. PINNs leverage the principles of physics to guide the learning process of neural networks, enabling them to approximate solutions to partial differential equations that govern fluid dynamics. This method significantly reduces the reliance on extensive datasets, making it particularly advantageous in scenarios where data is scarce or difficult to obtain. By incorporating physical laws directly into the loss function, PINNs ensure that the learned solutions adhere to the governing equations, boundary conditions, and initial conditions of the fluid system under consideration.
We established a PINNs model for solving incompressible fluid flow. The benchmark problem, cavity flow, was simulated using the proposed PINNs model. A special loss function in PINNs was suggested to allow an effect of utilization of noisy data. As a result, the cavity flow can be simulated using PINNs with less 100 velocity data. Also, as long as those data are allocated properly, no noise is found in solutions (see Satyadharma et al. [2]). Furthermore, PINNs can be used to estimate numerical error in CFD solutions due to different meshes. In addition, to estimate numerical error, it requires several fine mesh simulations. We also built a PINNs model which can estimate the error with a single simulation dataset. This can save more computational time to calculate numerical error in solutions. This abstract highlights the potential of PINNs to revolutionize traditional CFD methodologies, offering a promising pathway towards more efficient and reliable fluid dynamics simulations.
This work was supported by National Science and Technology Council (Grant no. NSTC 112-2221-E-011-075-MY3 and 112-2221-E-011-074-MY3) and National High Performance Computing Center Taiwan.
References
[1] Raissi, M., Perdikaris, P., Karniadakis, G. E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019).
[2] Satyadharma, A., Chern, M., Kan, H.C., Harinaldi, H., and Julian, J. Assessing Physics Informed Neural Network performance with sparse noisy velocity data. Physics of Fluids 36, 103619 (2024).
Bio: Prof. Ming-Jyh Chern is a Professor and Dean of Engineering at the National Taiwan University of Science and Technology. He earned his D.Phil. in Engineering Science from the University of Oxford in 1999, following his M.S. and B.S. degrees from National Taiwan University. With extensive experience in academia, he has served as an Associate Professor and Assistant Professor at his current institution, as well as a post-doctoral fellow at the Institute of Physics, Academia Sinica. His research interests encompass computational fluid dynamics, turbulence, and biomedical fluid dynamics, among others. He has published 70 SCI journal papers in his research area. Prof. Chern is actively involved in professional organizations and has held significant editorial and leadership roles, including President of TWSIAM. He has received numerous accolades, including keynote speaker invitations at international conferences and several best paper awards. Prof. Chern is also a principal investigator for various research projects funded by the Ministry of Science and Technology in Taiwan, contributing significantly to advancements in fluid dynamics and engineering education.
